You have a thought, and then you have some kind of emotional reaction to it, and that emotionally reaction should be felt in your body. Indeed, it is hard to have an emotion that doesn't have a physical component.

Say you think that you should call your mom, but then you feel a heaviness or a sinking in your gut, or a tightness in your neck or throat or jaw. These physical sensations are one of the main ways your subconscious tries to communicate with you. Let's further say that you don't know why you feel this way, and you can't say why you don't want to call your mom. You just find that you know you should call your mom but some part of you is giving you a really bad feeling about it. If you don't make an effort to untangle this mess, you'll probably just not call your mom, meaning whatever subconscious process originated those bad feelings in the first place will continue sitting under the surface and probably recapitulate the same reaction in similar situations.

If you gingerly try to "fit" the feeling with some words, as Gendlin says, the mind will either give you no feedback or it will give you a "yes, that's right" in the form of a further physical shift. This physical shift can be interpreted as the subconscious module acknowledging that its signal has been heard and ceasing to broadcast it.

I really don't think Gendlin is saying that the origin of your emotions about calling your mom is stored in your muscles. I think he's saying that when you have certain thoughts or parts of yourself that you have squashed out of consciousness with consistent suppression, these parts make themselves known through physical sensations, so it feels like it's in your body. And the best way to figure out what those feelings are is to be very attentive to your body, because that's the channel through which you're able to tentatively communicate with that part of yourself.

OR, it may not be that you did anything to suppress the thoughts, it may just be that the mind is structured in such a way that certain parts of the mind have no vocabulary with which to just inject a simple verbal thought into awareness. There's no reason a priori to assume that all parts of the mind have equal access to the phenological loop.

Maybe Gendlin's stuff is easier to swallow if you happen to already have this view of the conscious mind as the tip of the iceberg, with most of your beliefs and habits and thoughts being dominated by the vast but unreflective subconscious. If you get into meditation in any serious way, you can really consistently see that these unarticulated mental constructs are always lurking there, dominating behavior, pushing and pulling. To me, it's not woo at all, it's very concrete and actionable, but I understand that Gendlin's way of wording things may serve as a barrier to entry.